A car is parked on a cliff overlooking the ocean on an incline that makes an ang

Question

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 21.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.37 m/s2 for a distance of 55.0 m to the edge of the cliff, which is 30.0 m above the ocean. (a) Find the car's position relative to the base of the cliff when the car lands in the ocean. (b) Find the length of time the car is in the air.

Explanation / Answer

a)angle of incline with horizon=21o below horizon

acceleration=3.37m/s2

Distance travelled along incline=55m

velocity of the car at the edge of cliff = sqrt(2*3.37*55)=19.25m/s

angle the velocity makes with the horizon=21o

horizontal component of velocity=19.25cos21=17.97 m/s

vertical component of velocity =19.25sin21=6.9m/s

Height of edge of cliff from river=30m

Vertical velocity of car when it just reached ocean can be determined as

v2=u2+2as

v2=6.92+(2*9.8*30) = 635.61

v=25.21m/s

time taken by car to reach ocean = (25.21-6.9)/9.8=1.87 seconds

Horizontal distance travelled by car in 1.87 seconds=17.97*1.87=33.6m

Car's position relative to base of cliff = 33.6m (horizontally)

b)The time the car is in the air=1.87 seconds

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